Hansen–Jagannathan bound
The Hansen-Jagannathan (HJ) bound is a concept in finance that helps us understand how good a particular asset pricing model is at explaining the variation in returns on different assets. It tells us if the model is "reasonable" or "unreasonable" in terms of its ability to explain what's going on in the financial markets.
Okay, imagine you have a bunch of candies in front of you - red, blue, green, yellow, and so on. You have a friend who thinks they can predict how many you'll eat of each color. They might say, "I think you'll eat twice as many blue candies as green candies." That's their prediction, based on some idea they have in their head of how much you like each color.
Now, let's say you start eating the candies, and you keep track of how many of each color you eat. At the end, you can compare your friend's prediction to what actually happened. If your friend was really good at predicting your candy-eating habits, their prediction would be very close to the actual result. But if they were really bad at predicting, it might be way off.
Similarly, in finance, we have models that try to predict returns on different stocks. The Hansen-Jagannathan bound helps us evaluate how good those models are at predicting what actually happens in the stock market.
The Hansen-Jagannathan bound says that if the model is "reasonable," it should be possible to find a "risk factor" that explains the returns on all the stocks in the market. A risk factor is something that affects all stocks in the same way - for example, changes in interest rates might affect all stocks similarly.
If the model is not "reasonable," then there won't be any risk factor that can explain the returns on all stocks. That means the model isn't doing a good job of capturing what's actually happening in the market.
So, think of the Hansen-Jagannathan bound like a way to check if someone's prediction about your candy-eating habits is good or bad. It helps us evaluate whether a financial model is doing a good job of predicting stock returns.
Okay, imagine you have a bunch of candies in front of you - red, blue, green, yellow, and so on. You have a friend who thinks they can predict how many you'll eat of each color. They might say, "I think you'll eat twice as many blue candies as green candies." That's their prediction, based on some idea they have in their head of how much you like each color.
Now, let's say you start eating the candies, and you keep track of how many of each color you eat. At the end, you can compare your friend's prediction to what actually happened. If your friend was really good at predicting your candy-eating habits, their prediction would be very close to the actual result. But if they were really bad at predicting, it might be way off.
Similarly, in finance, we have models that try to predict returns on different stocks. The Hansen-Jagannathan bound helps us evaluate how good those models are at predicting what actually happens in the stock market.
The Hansen-Jagannathan bound says that if the model is "reasonable," it should be possible to find a "risk factor" that explains the returns on all the stocks in the market. A risk factor is something that affects all stocks in the same way - for example, changes in interest rates might affect all stocks similarly.
If the model is not "reasonable," then there won't be any risk factor that can explain the returns on all stocks. That means the model isn't doing a good job of capturing what's actually happening in the market.
So, think of the Hansen-Jagannathan bound like a way to check if someone's prediction about your candy-eating habits is good or bad. It helps us evaluate whether a financial model is doing a good job of predicting stock returns.